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title: "A transparent rectangular tank contains two immiscible liquids at rest. The upper liquid layer has thickness 3d and index of refraction n_1 = 1.50, while the lower liquid layer has thickness 4d and index of refraction n_2 = 4/3. A small coin rests at the bottom of the tank directly beneath both liquid layers. An observer in air (n_air = 1.00) looks down at the coin from directly above along a line of sight nearly perpendicular to the upper liquid surface. What is the ratio of the coin’s total apparent depth to its actual depth, d_apparent / d_actual?"
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url: "https://nerd-notes.com/ubq/123339/"
date_modified: "2026-09-28T11:58:11+00:00"
---

# A transparent rectangular tank contains two immiscible liquids at rest. The upper liquid layer has thickness 3d and index of refraction n_1 = 1.50, while the lower liquid layer has thickness 4d and index of refraction n_2 = 4/3. A small coin rests at the bottom of the tank directly beneath both liquid layers. An observer in air (n_air = 1.00) looks down at the coin from directly above along a line of sight nearly perpendicular to the upper liquid surface. What is the ratio of the coin’s total apparent depth to its actual depth, d_apparent / d_actual?

A transparent rectangular tank contains two immiscible liquids at rest. The upper liquid layer has thickness 3d and index of refraction n_1 = 1.50, while the lower liquid layer has thickness 4d and index of refraction n_2 = 4/3. A small coin rests at the bottom of the tank directly beneath both liquid layers. An observer in air (n_air = 1.00) looks down at the coin from directly above along a line of sight nearly perpendicular to the upper liquid surface. What is the ratio of the coin's total apparent depth to its actual depth, d_apparent / d_actual?

![A cross-sectional schematic diagram of an open rectangular tank viewed from the side. The tank rests on a flat horizontal surface. Inside the tank are two distinct horizontal fluid layers separated by a horizontal interface line. The top layer has a vertical double-headed dimension arrow labeled 3d on the left and is labeled n_1 = 1.50 in its center with light-gray diagonal hatching. The bottom layer has a vertical double-headed dimension arrow labeled 4d on the left and is labeled n_2 = 4/3 in its center with unshaded fill. A small solid black circle representing a coin rests centered on the bottom floor of the tank. Above the top surface of the liquid, in the air region labeled n = 1.00, an eye icon looks vertically downward toward the coin along a vertical dashed line. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596691-CZEDxD.jpg)

- **A.** \(\dfrac{2}{3}\)
- **B.** \(\dfrac{12}{17}\)
- **C.** \(\dfrac{5}{7}\)
- **D.** \(\dfrac{3}{4}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123339/*